where \(\mathcal {L}_d(\cdot )\)  is a proper discrimination loss function such as cross-entropy and \(\mathbb {E}(\cdot )\)  denotes the probability expectation operator. Upon training the base deep network model on the dataset \(\mathcal {D}^{0}\) , the PAD system is fielded for testing. We have depicted this base model as the PAD Module in Figure REF .
If \(n_0\)  is large enough, the selected deep network structure is suitable, and observed data during testing are drawn from the training distribution \(q^{0}(\mathbf {x})\)  then the model will generalize well during execution according to theoretical guarantees of PAC-learning framework [1]}. However, if new types of attacks are introduced after the initial training or any drift in the input distribution occurs, poor model generalization is expected. In other words, the model may fail to identify new attack types and misclassify them as bona-fide samples.
